I believe that in their mindset, same-sex relationships harm the people involved, directly, by some combination of personal degradation (moral erosion?) and otherwise separating them from God. If you believe that a personal relationship with God is more important than anything that can be found in the material, emotional or intellectual worlds, that's the greatest harm that can be done to somebody. Not my belief, of course. I'm an atheist. But I think it's roughly theirs.

By that viewpoint, same-sex marriage is awful for the people involved (distancing them from God and morality) and for society (providing an example of "harmless" distancing from God and morality). This is also roughly the same logic by which Rock music was called Devil Music, so obviously you can go to (what we now consider, fiftyish years later) some silly extremes.

But I come from the South, where these ideas aren't as culturally or temporally distant as they are in California or the East Coast.